calculating work from to pump water over the top of a trough

A water trough is 6 feet long, its vertical cross section is as isosceles trapezoid with lower base 2 feet, upper base 3 feet and altitude 2 feet. if the trough is full, how much work is done in pumping all of the water over the top of the trough? Use 62.5 lb/ft^3 as the weight density factor for water.

A water trough is 6 feet long, its vertical cross section is as isosceles trapezoid with lower base 2 feet, upper base 3 feet and altitude 2 feet. if the trough is full, how much work is done in pumping all of the water over the top of the trough? Use 62.5 lb/ft^3 as the weight density factor for water.

Here are the steps you need to solve the problem:

Consider a horizontal cross-section through the water at a height above the base, and with thickness ..

Work out the area of this cross-section in terms of , and hence its mass in terms of and ..

This mass of water is raised through a vertical height of feet. Find an expression for the work done, , when this happens..

Write down an expression for , and hence, by integrating between and , evaluate the total work done.